Problem: Let $g(x)=15\cdot4^x$. Find $g'(x)$. Choose 1 answer: Choose 1 answer: (Choice A) A $15\log_4(x)\cdot 4^x$ (Choice B) B $60^x\cdot \ln(4)$ (Choice C) C $15\ln(4)\cdot 4^x$ (Choice D) D $60^x\cdot \ln(x)$
Answer: The expression for $g(x)$ includes an exponential term. Remember that the derivative of the general exponential term $a^x$ (where $a$ is any positive constant) is $\ln(a)\cdot a^x$. Put another way, $\dfrac{d}{dx}(a^x)=\ln(a)\cdot a^x$. $\begin{aligned} g'(x)&=\dfrac{d}{dx}(15\cdot4^x) \\\\ &=15\dfrac{d}{dx}(4^x) \\\\ &=15\cdot\ln(4)\cdot4^x \\\\ \end{aligned}$ In conclusion, $g'(x)=15 \ln(4)\cdot4^x$.